Excursions of diffusion processes and continued fractions

被引：5

作者：

Comtet, Alain ^{[1
,2
]}

Tourigny, Yves ^{[3
]}

机构：

[1] Univ Paris 11, Lab Phys Theor & Modeles Stat, F-91405 Orsay, France

[2] Univ Paris 06, Inst Henri Poincare, F-75005 Paris, France

[3] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2011年 / 47卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Diffusion processes; Continued fraction; Riccati equation; Excursions; Stieltjes transform; ONE-DIMENSIONAL DIFFUSIONS; CLASSICAL DIFFUSION; DEATH PROCESSES; BIRTH;

D O I：

10.1214/10-AIHP390

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

It is well-known that the excursions of a one-dimensional diffusion process can be studied by considering a certain Riccati equation associated with the process. We show that, in many cases of interest, the Riccati equation can be solved in terms of an infinite continued fraction. We examine the probabilistic significance of the expansion. To illustrate our results, we discuss some examples of diffusions in deterministic and in random environments.

引用

页码：850 / 874

页数：25

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